Divine Lensmaker's Equation Derivation

Its not mandatory but it makes the derivation.

Lensmaker's equation derivation. Using lens formula the equation for magnification can also be obtained as m h2h1 vu f-vf f fu This equation is valid for both convex and concave lenses and for. SF017 SF027 51 15 Thin Lenses Formula and Lens makers Equation Considering the ray diagram of refraction for 2 spherical surfaces as shown in figure below. Substituting 13 into 12 gives It can be shown that equations 12 13 and 14 are applicable to all thin lenses through the use of.

The complete derivation of lens maker formula is described below. 13 from Schroeder 1987. The lensmakers equation relates the focal length of a simple lens with the spherical curvature of its two faces where and represent the radii of curvature of the lens surfaces closest to the light source on the left and the object on the right.

Commonly it is given in the thin-lens limit where it is assumed that the thickness of the lens is small compared to the object and image distances. It is used by lens manufacturers to make the lenses of particular power from the glass of a given refractive index. The lensmakers formula relates the index of refraction the radii of curvature of the two surfaces of the lens and the focal length of the lens.

The lens makers equation is another formula used for lenses that give us a relationship between the focal length refractive index and radii of curvature of the two spheres used in lenses. Equation 13 is called the lensmakers equation. Here the tip of the object involves a small deviation from the.

The focal length of a thick lens in air can be calculated from the lensmakers equation. Applying the equation of paraxial refraction with air to each surface gives. Using the formula for refraction at a single spherical surface we can say that For the first surface For the second surface Now adding equation 1 and 2 When u and v f.

A number of idealizations simplifications and approximations are used to complete the derivation but the results are compact and sufficiently accurate for most purposes. O C 1 II C 2 1 P 1 P 2 I2 B E A D u1 v1 v2 r1 r2 t n1 t v1 n2 n1 SF027 52 By using the equation of spherical refracting surface the refraction by first surface AB and second surface DE are given by. The LibreTexts libraries are Powered by MindTouch and are supported by the Department of Education Open Textbook Pilot Project the UC Davis Office of the Provost the UC Davis Library the California State University Affordable Learning Solutions Program and.